Summary: NONEXISTENCE OF REFLEXIVE IDEALS IN
IWASAWA ALGEBRAS OF CHEVALLEY TYPE
K. ARDAKOV, F. WEI AND J. J. ZHANG
Abstract. Let # be a root system and let #(Zp ) be the standard Chevalley
Zp ­Lie algebra associated to #. For any integer t # 1, let G be the uniform
pro­p group corresponding to the powerful Lie algebra p t #(Zp ) and suppose
that p # 5. Then the Iwasawa
algebra# G has no nontrivial two­sided reflexive
ideals. This was previously proved by the authors for the root system A 1 .
0. Introduction
0.1. Prime ideals in Iwasawa algebras. One of the main projects in the study
of noncommutative Iwasawa algebras aims to understand the structure of two­sided
ideals in Iwasawa algebras #G
and# G for compact p­adic analytic groups G. A list
of open questions in this project was posted in a survey paper by the first author
and Brown [AB]. Motivated by its connection to the Iwasawa theory of elliptic
curves in arithmetic geometry it is particularly interesting to understand the prime
ideals of #G when G is an open subgroup of GL 2 (Z p ). A reduction [A] shows that
this amounts to understanding the prime ideals
of# G when G is an open subgroup

Source: Ardakov, Konstantin - School of Mathematical Sciences, University of Nottingham

Collections: Mathematics